On the equivalence between least-squares and kernel approximations in meshless methods

CMES - Computer Modeling in Engineering and Sciences

Volumn 2, Issue 4, 2001, Pages 447-462

  Jin, Xiaozhong ^b   Li, Gang ^b   Aluru, N R ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000250655     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Aluru N.R. (2000): A point collocation method based on reproducing kernel approximations, Int. J. Numer. Methods in Engrg., Vol. 47, pp. 1083-1121.
2. Aluru N.R., Li G. (2001): Finite Cloud Method: A true meshless technique based on a fixed reproducing kernel approximation, Int. J. Numer. Methods in Engrg., Vol. 50, No. 10, pp. 2373-2410.
3. Atluri S.N., Zhu T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, Vol. 22, pp. 117-127.
4. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. (1996): Meshless methods: An overview and recent developments, Comput. Methods Appl. Mech. Engrg., Vol. 139, pp. 3-47.
5. Belytschko T., Lu Y.Y., Gu L. (1994): Element free Galerkin methods, Int. J. Numer Methods in Engrg., Vol. 37, pp. 229-256.
6. Chen J.-S., Pan C., Wu C., Liu W.K. (1996): Reproducing kernel particle methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Engrg., Vol. 139, pp. 195-227.
7. Duarte C.A., Oden J.T. (1996): An h-p adaptive method using clouds,Comput. Methods in Appl. Mech. Engrg., Vol. 139, pp. 237-262.
8. Kim H.G., Atluri S.N. (2000): Arbitrary Placement of Secondary Nodes and Error Control in the Meshless Local Petrov-Galerkin (MLPG) Method, CMES: Computer Modeling in Engineering & Sciences, Vol. 1,No.3, pp. 11-32.
9. Lin H., Atluri S.N. (2000): Meshless Local Petrov-Galerkin (MLPG) Method for Convection - Diffusion Problems, CMES: Computer Modeling in Engineerng & Sciences, Vol. 1,No.2, pp. 45-60.
10. Liu W.K., Jun S., Li S., Adee J., Belytschko T. (1995): Reproducing kernel particle methods for structural dynamics, Int. J. Numer Methods in Engrg., Vol. 38, pp. 1655-1679.
11. Mukherjee Y.X., Mukherjee S. (1997): The boundary node method for potential problems, Int. J. Numer. Methods Engrg., Vol. 40, pp. 797-815.
12. Oñate E., Idelsohn S., Zienkiewicz O.C., Taylor R.L. (1996): A finite point method in computational mechanics. Applications to convective transport and fluid flow, Int. J. Numer. Methods in Engrg., Vol. 39, pp. 3839-3866.
13. Oñate E., Idelsohn S., Zienkiewicz O.C., Taylor R.L., Sacco C., (1996): A stabilized finite point method for analysis of fluid mechanics problems, Comput. Methods Appl. Mech. Engrg., Vol. 139, pp. 315-346.
14. Oñate E., Idelsohn S. (1998): A mesh-free finite point method for advective-diffusive transport and fluid flow problems, Computational Mechanics, Vol. 21, pp. 283-292, 1998.
15. Wordelman C., Aluru N.R., Ravaioli U. (2000): A meshless method for the numerical solution of the 2-and 3-D semiconductor Poisson equation, Computer Modeling in Engineering & Sciences, Vol. 1, No. 1, pp. 123-128.
16. Zhu T., Zhang J.-D., Atluri S.N. (1998): A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach, Computational Mechanics, Vol. 21, pp. 223-235.